3(x-2)(x-2)+4=10

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Solution for 3(x-2)(x-2)+4=10 equation: 


Simplifying
3(x + -2)(x + -2) + 4 = 10

Reorder the terms:
3(-2 + x)(x + -2) + 4 = 10

Reorder the terms:
3(-2 + x)(-2 + x) + 4 = 10

Multiply (-2 + x) * (-2 + x)
3(-2(-2 + x) + x(-2 + x)) + 4 = 10
3((-2 * -2 + x * -2) + x(-2 + x)) + 4 = 10
3((4 + -2x) + x(-2 + x)) + 4 = 10
3(4 + -2x + (-2 * x + x * x)) + 4 = 10
3(4 + -2x + (-2x + x2)) + 4 = 10

Combine like terms: -2x + -2x = -4x
3(4 + -4x + x2) + 4 = 10
(4 * 3 + -4x * 3 + x2 * 3) + 4 = 10
(12 + -12x + 3x2) + 4 = 10

Reorder the terms:
12 + 4 + -12x + 3x2 = 10

Combine like terms: 12 + 4 = 16
16 + -12x + 3x2 = 10

Solving
16 + -12x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
16 + -10 + -12x + 3x2 = 10 + -10

Combine like terms: 16 + -10 = 6
6 + -12x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
6 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
2 + -4x + x2 = 0

Solving
2 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -4x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4x + x2 = 0 + -2
-4x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4x + x2 = -2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -2 + 4

Reorder the terms:
4 + -4x + x2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4x + x2 = 2

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -2) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -2 = 1.414213562

Simplifying
x + -2 = 1.414213562

Reorder the terms:
-2 + x = 1.414213562

Solving
-2 + x = 1.414213562

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.414213562 + 2
x = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
x = 3.414213562

Simplifying
x = 3.414213562


Subproblem 2
x + -2 = -1.414213562

Simplifying
x + -2 = -1.414213562

Reorder the terms:
-2 + x = -1.414213562

Solving
-2 + x = -1.414213562

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.414213562 + 2
x = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
x = 0.585786438

Simplifying
x = 0.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.414213562, 0.585786438}
Solution
x = {3.414213562, 0.585786438}

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